Question

What is the cost of operating a 3.00-Welectric clock for a year if the cost of electricity is $0.0900 kW.h?

Short answer

The cost of operation electric clock for a year is $2.37.

Step-by-step solution

Power

Power is defined as the rate at which energy is expended.

The power is defined as,

\(P = \frac{E}{T}\) (1.1)

Here, E is the energy consumed and T is the time.

Rearranging equation (1.1) in order to get an expression for the energy consumption,

E=PT (1.2)

The commercial unit of energy is kilowatt-hour (kW.h).

Find the cost of operation electric clock for a year

The energy consumption of an 3.00-W electric clock in a year can be calculated using equation (1.2).

Putting all known values in equation (1.2),

\(\begin{aligned}E &= \left( {3.00{\rm{ W}}} \right) \times \left( {1{\rm{ year}}} \right)\\ &= \left( {3.00{\rm{ W}}} \right) \times \left( {\frac{{1{\rm{ kW}}}}{{1000{\rm{ W}}}}} \right) \times \left( {1{\rm{ year}}} \right) \times \left( {\frac{{365{\rm{ day}}}}{{1{\rm{ year}}}}} \right) \times \left( {\frac{{24{\rm{ h}}}}{{1{\rm{ day}}}}} \right)\\ &= 26.28{\rm{ kW}} \cdot {\rm{h}} \end{aligned}\)

Since, the cost of electricity is $0.0900 per kW.h. Therefore, cost of operation of an electric clock for a year is,

\(\begin{aligned}{\rm{Cost}} = {\rm{Rate}} \times E \end{aligned}\)

Putting all known values,

\(\begin{aligned}{\rm{Cost}} &= \left( {\$ 0.0900{\rm{ per kW}} \cdot {\rm{h}}} \right) \times \left( {26.28{\rm{ kW}} \cdot {\rm{h}}}\right)\\\approx \$ 2.37\end{aligned}\)

Therefore, the required cost of operation electric clock for a year is $2.37.